A fuel injector having a valve housing in which a piezoelectric armature and an hydraulic coupler are arranged has already been proposed in German Patent Application No. 103 60 449, the piezoelectric actuator having a positive pole and an earth pole, an electrical plug with a positive terminal and a ground terminal being provided on the valve housing for the contacting with a voltage source. Via a cable in each case, the positive pole of the piezoelectric actuator is connected to the positive terminal of the plug, and the earth pole of the piezoelectric actuator is connected to the ground terminal of the plug. Since the hydraulic coupler between the valve housing and the actuator is arranged in a section of the fuel injector that faces the plug, the cables originating from the plug must be guided around the coupler to reach the actuator. Due to the fact that the hydraulic coupler executes thermally caused compensating movements, the cables cannot be taut, but must be non-tensioned by providing additional length. The cables are not allowed to be in contact with adjacent components, since the many compensating movements may otherwise cause them to fray over time. It is disadvantageous that the compensating movements put heavy mechanical stress on the cables, so that a cable fracture as a result of material fatigue will occur after a predefined service life of the fuel injector, or the solder or welding points of the cables will tear. This leads to malfunctioning of the fuel injector.